Question

This is a graph of y=x³.

How do we shift the graph of y=x^3 to get the graph of y=(x-2)³-4?

Answer 1

2 right, 4 down

Explanation:

By subtracting 2 inside the function, the graph is shifted 2 to the right and by subtracting 4, it is shifted 4 down.

To think of this more intuitively, in the original function, inputting 0 would yield the same output as plugging in a function with (x - 2) inside:

`x^3=0^3=0\\(x-2)^3=(2-2)^3=0^3=0`

In addition, by subtracting -4, the value would always go down 4 from the original value of x^3:

`x^3 = 0^3 = 0`

`x^3-4 = 0^3-4=0-4=-4`

By putting these together we get the answer above.